At a crucial moment in Euripides’ Andromache, the title character throws her hands (περὶ χεῖρε βαλοῦσα, 115) around a statue of the goddess Thetis and laments the losses that have brought her to a point of desperation and despair. When Thetis appears at the end of the play, she answers Andromache’s pleas and grants her a renewed life of marriage and motherhood. Yet in her embrace of the statue, Andromache momentarily embodies an alternative impulse: a longing to merge with the stony form of the goddess and to cease from the patterns of nuptial mobility and sexual reproduction that have defined her life thus far. In this article, I argue that we should understand this embrace as “queer”—as a moment of intimate contact between mortal woman and immortal goddess that deeply unsettles the models of sexual and reproductive order that dominate Greek art and literature. While the play ends by redirecting Andromache toward the propagation of the Trojan line, the queer potential of that crucial embrace is taken up by Thetis herself, who re-scripts her own marriage to Peleus in a way that both inverts gendered patterns of movement and rejects the valorization of female fertility. Euripides’ Andromache thus concludes with the restoration of mortal sexual and reproductive order, yet through Andromache’s encounter with Thetis, it also gestures to the queer and startling freedom of a barren future.